Uncertainty estimation of non-ideal analog switches using programmable Josephson voltage standards for mutual inductance measurement in the joule balance

Abstract

Measurement of the mutual inductance is one of the key techniques in the joule balance to determine the Planck constant h, where a standard-square-wave compensation method was proposed to accurately measure the dc value of the mutual inductance. With this method, analog switches are used to compose an analog-switch signal generator to synthesize the excitation and compensation voltages. However, the accuracy of the compensation voltage is influenced by the non-ideal behaviors of analog-switches. In this paper, the effect from these non-ideal switches is analyzed in detail and evaluated with the equivalent circuits. A programmable Josephson voltage standard (PJVS) is used to generate a reference compensation voltage to measure the time integration of the voltage waveform generated by the analog-switch signal generator. Moreover, the effect is also evaluated experimentally by comparing the difference between the mutual inductance measured with the analog-switch signal generator and the value determined by the PJVS-analog-switch generator alternately in the same mutual inductance measurement system. The result shows that the impact of analog switches is 1.97 × 10 −7 with an uncertainty of 1.83 × 10 −7 (k = 1) and confirms that the analog switch method can be used regularly instead of the PJVS in the mutual inductance measurement for the joule balance experiment.